Embedded Rayleigh-Bloch surface waves along periodic rectangular arrays

R Porter, DV Evans

Research output: Contribution to journalArticle (Academic Journal)peer-review

100 Citations (Scopus)


In this paper, surface waves in the presence of an infinite periodic array of obstacles of rectangular cross-section are considered. Rayleigh-Bloch surface waves are described by a localised wave motion which does not propagate energy away from the array. The periodicity of the array implies the existence of a cut-off frequency below which Rayleigh-Bloch surface waves may be sought. Such solutions are well established and Rayleigh-Bloch surface waves have been shown to exist for all rectangular cross-section. In the present paper, we generate examples of Rayleigh-Bloch surface waves for the more complicated case of frequencies lying above the first cut-off, such waves correspond mathematically to eigenvalues embedded in the continuous spectrum of the field operator. Numerical results are given for rectangular cross-sections based on an integral equation formulation of the problem. Finally, strong numerical evidence is given for embedded Rayleigh-Bloch waves that exist for a single family of rectangular cross-section above the second cut-off. (C) 2005 Elsevier B.V. All rights reserved.
Translated title of the contributionEmbedded Rayleigh-Bloch surface waves along periodic rectangular arrays
Original languageEnglish
Pages (from-to)29 - 50
JournalWave Motions
Volume43 (1)
Publication statusPublished - Nov 2005

Bibliographical note

Publisher: Elsevier Science BV
Other identifier: IDS Number: 967BI


Dive into the research topics of 'Embedded Rayleigh-Bloch surface waves along periodic rectangular arrays'. Together they form a unique fingerprint.

Cite this